Question

the table shows the distance traveled over time while traveling at a constant speed.

distance vs. time
\

$$\begin{tabular}{|c|c|} \\hline time in minutes (x) & distance in meters (y) \\\\ \\hline 1 & 1,200 \\\\ \\hline 2 & 2,400 \\\\ \\hline 3 & 3,600 \\\\ \\hline 4 & 4,800 \\\\ \\hline \\end{tabular}$$

what is the rate of change in the y-values with respect to the x-values?

• \\(\frac{1}{900}\\) minutes per meter
• \\(\frac{1}{1,200}\\) minutes per meter
• 900 meters per minute
• 1,200 meters per minute

Explanation:

⚡ Using what you learned: Rate of Change and Applications

Step 1: Identify coordinates

Select two points from the table \((x, y)\):

$$ (1, 1200) $$

$$ (2, 2400) $$

Step 2: Calculate rate of change

$$ \text{Rate of Change} = \frac{y_2 - y_1}{x_2 - x_1} $$

$$ \text{Rate of Change} = \frac{2400 - 1200}{2 - 1} = 1200 $$

Step 3: Determine units

The \(y\)-values represent distance in meters, and the \(x\)-values represent time in minutes.

$$ \text{Units} = \text{meters per minute} $$

Answer:

\(1,200\) meters per minute